Chapter Eight: Regular Expression Applications Formal Language, chapter 8, slide 1 1
We have seen some of the implementation techniques related to DFAs and NFAs. These important techniques are like tricks of the programmer's trade, normally hidden from the end user. Not so with regular expressions: they are often visible to the end user, and part of the user interface of a variety of useful software tools. Formal Language, chapter 8, slide 2 2
Outline 8.1 The egrep Tool 8.2 Non-Regular Regexps 8.3 Implementing Regexps 8.4 Regular Expressions in Java 8.5 The lex Tool Formal Language, chapter 8, slide 3 3
Text File Search Unix tool: egrep Searches a text file for lines that contain a substring matching a specified pattern Echoes all such lines to standard output Formal Language, chapter 8, slide 4 4
Example: A Constant Substring File names: fred barney wilma betty egrep command and results: % egrep 'a' names barney wilma % Formal Language, chapter 8, slide 5 5
More Than Simple Substrings egrep understands a language of patterns Various dialects of its pattern-language are also used by many other tools Confusingly, these patterns are often called regular expressions, but they differ from ours To keep the two ideas separate, we'll call the text patterns used by egrep and other tools by their common nickname: regexps Formal Language, chapter 8, slide 6 6
A Regexp Dialect * like our Kleene star: for any regexp x, x* matches strings that are concatenations of zero or more strings from the language specified by x like our +: for any regexps x and y, x y matches strings that match either x or y (or both) () used for grouping ^ this special symbol at the start of the regexp allows it to match only at the start of the line $ this special symbol at the end of the regexp allows it to match only at the end of the line. matches any symbol (except the end-of-line marker) Formal Language, chapter 8, slide 7 7
Example File names: fred barney wilma betty egrep for a, followed by any string, followed by y: % egrep 'a.*y' names barney % Formal Language, chapter 8, slide 8 8
Example File names: fred barney wilma betty egrep for odd-length string; what went wrong? % egrep '.(..)*' names fred barney wilma betty % Formal Language, chapter 8, slide 9 9
Example File names: fred barney wilma betty egrep for odd-length line: % egrep '^.(..)*$' names fred barney wilma betty % Formal Language, chapter 8, slide 10 10
Example File numbers: 0 1 10 11 100 101 110 111 1000 1001 1010 egrep for numbers divisible by 3: % egrep '^(0 1(01*0)*1)*$' numbers 0 11 110 1001 % Formal Language, chapter 8, slide 11 11
Outline 8.1 The egrep Tool 8.2 Non-Regular Regexps 8.3 Implementing Regexps 8.4 Regular Expressions in Java 8.5 The lex Tool Formal Language, chapter 8, slide 12 12
Capturing Parentheses Many regexp dialects can define more than just the regular languages Capturing parentheses: \( r \) captures the text that was matched by the regexp r \n matches the same text captured by the nth previous capturing left parenthesis Found in grep (but not most versions of egrep) Formal Language, chapter 8, slide 13 13
Example File test: abaaba ababa abbbabbb abbaabb grep for lines that consist of doubled strings: % grep '^\(.*\)\1$' test abaaba abbbabbb % Formal Language, chapter 8, slide 14 14
More Than Regular The formal language corresponding to that example is {xx x Σ*} It turns out that this language is not regular Like DFAs, regular expressions can do only what you could implement in a computer using a fixed, finite amount of memory Capturing parentheses must remember a string whose size is unbounded We'll see this more formally later Formal Language, chapter 8, slide 15 15
Outline 8.1 The egrep Tool 8.2 Non-Regular Regexps 8.3 Implementing Regexps 8.4 Regular Expressions in Java 8.5 The lex Tool Formal Language, chapter 8, slide 16 16
Many Regexp Tools Many programs make use of regexp dialects: Text tools like emacs, vi, and sed Compiler construction tools like lex Programming languages like Perl, Ruby, and Python Program language libraries like those for Java and the.net languages How do all these systems implement regexp matching? Formal Language, chapter 8, slide 17 17
Implementing Regexps We've already seen how, roughly: Convert regexp to an NFA Simulate that Or, convert to DFA and simulate that Many implementation tricks are possible; we haven't worried much about efficiency And some important details are different because regexps are used to match substrings Formal Language, chapter 8, slide 18 18
Using a DFA Our basic DFA decides after it reads the whole string For regexps, we need to find whether any substring is accepted That means running the DFA repeatedly, on each successive starting position Run the DFA until: it enters an accepting state: that's a match enters a non-accepting trap state: restart the DFA from the next possible starting position hits the end of the string: restart the DFA from the next possible starting position Formal Language, chapter 8, slide 19 19
Which Match? Some tools needs to know which substring matched Capturing parentheses, for example If there is more than one match in a given string, which should the tool find? The string abcab contains two substrings that match the regexp ab It isn't enough to specify the leftmost match: what if several matches start at the same place? The string abb contains three substrings that match the regexp ab*, and they all start at the first symbol Formal Language, chapter 8, slide 20 20
Longest Leftmost Some tools are required to find the longest leftmost match in a string The string abbcabb contains six matches for ab* The first abb is the longest leftmost match That means running the DFA past accepting states Run the DFA starting from each successive position, until it enters a non-accepting trap or hits the end As you go, keep track of the last accepting state entered, and the string position at the time At the end of this iteration, if any accepting state was recorded, that is the longest leftmost match Formal Language, chapter 8, slide 21 21
Using an NFA Similar accommodations are required Run from each successive starting position When an implementation using backtracking finds a match, it cannot necessarily stop there If the longest match is required, it must remember the match and continue Explore all paths through the NFA to make sure the longest match is found Formal Language, chapter 8, slide 22 22
Outline 8.1 The egrep Tool 8.2 Non-Regular Regexps 8.3 Implementing Regexps 8.4 Regular Expressions in Java 8.5 The lex Tool Formal Language, chapter 8, slide 23 23
java.util.regex The Java package java.util.regex contains classes for working with regexps in Java Two particularly important ones: The Pattern class A compiled version of a regexp, ready to be given an input string to test A bit like a Java representation of an NFA The Matcher class Has a Pattern, an input string to run it on, and the current state of the search for a match Can find matches within a string and report their locations Formal Language, chapter 8, slide 24 24
Example A mini-grep written in Java We'll take a regexp from the command line, and make it into a Pattern Then, for each line of the standard input: we'll make a Matcher for that line and use it to test for a match with our Pattern If it matches, we'll echo the line to the standard output Formal Language, chapter 8, slide 25 25
import java.io.*; import java.util.regex.*; /** * A Java application to demonstrate the Java package * java.util.regex. We take one command-line argument, * which is treated as a regexp and compiled into a * Pattern. We then use that pattern to filter the * standard input, echoing to standard output only * those lines that match the Pattern. */ Formal Language, chapter 8, slide 26 26
class RegexFilter { public static void main(string[] args) throws IOException { Pattern p = Pattern.compile(args[0]); // the regexp BufferedReader in = // standard input new BufferedReader(new InputStreamReader(System.in)); // Read and echo lines until EOF. } } String s = in.readline(); while (s!=null) { Matcher m = p.matcher(s); if (m.matches()) System.out.println(s); s = in.readline(); } Formal Language, chapter 8, slide 27 27
Example, Continued Now this Java application can be used to do our divisible-by-three filtering: % java RegexFilter '^(0 1(01*0)*1)*$' < numbers 0 11 110 1001 % Formal Language, chapter 8, slide 28 28
Outline 8.1 The egrep Tool 8.2 Non-Regular Regexps 8.3 Implementing Regexps 8.4 Regular Expressions in Java 8.5 The lex Tool Formal Language, chapter 8, slide 29 29
Preconstructing Automata Applications like grep take a regexp as user input: Convert regexp to automaton Simulate the automaton on a text file Discard automaton when finished Other applications, like compilers, use the same regexp and automaton each time It would be a waste of time to do the regexp-to-automaton conversion each time the compiler is run Formal Language, chapter 8, slide 30 30
The lex Tool lex preconstructs automata: Regexps as input C source code for a DFA as output Similar tools exist for many other output languages Useful for applications like compilers that use the same set of regexps over and over Formal Language, chapter 8, slide 31 31
The lex Input File definition section %% rules section %% user subroutines Definition section: a variety of preliminary definitions User subroutines: C code for extra C functions used from inside the rules section In our examples, both these sections will be empty: %% rules section %% Formal Language, chapter 8, slide 32 32
Rules Section %% abc {fprintf(yyout, "Found one.\n");}. \n {} %% The rules section is a list of regexps Each regexp is followed by some C code, to be executed whenever a match is found This example has two regexps with code Formal Language, chapter 8, slide 33 33
First regexp: abc Rules Section %% abc {fprintf(yyout, "Found one.\n");}. \n {} %% Action when abc is matched: print a message to the current output file (yyout), which is the standard output in this case Formal Language, chapter 8, slide 34 34
Rules Section %% abc {fprintf(yyout, "Found one.\n");}. \n {} %% Second regexp:. \n. matches any symbol except end-of-line \n matches end-of-line Action when. \n is matched: do nothing The string abc matches both regexps, but the lexgenerated code goes with the longest match Formal Language, chapter 8, slide 35 35
Running lex % flex abc.l % gcc lex.yy.c -o abc ll % Assuming our example is stored as abc.l flex is the gnu implementation of lex C code output by flex is stored in lex.yy.c The gcc command compiles the C code It puts the executable in abc (because of -o abc) It links with the special lex library (because of -ll) Formal Language, chapter 8, slide 36 36
Running The lex Program Suppose abctest contains these lines: abc aabbcc abcabc Then our lex program does this: % abc < abctest Found one. Found one. Found one. % Formal Language, chapter 8, slide 37 37
Example %% ^(0 1(01*0)*1)*$ {fprintf(yyout, "%s\n", yytext);}. \n {} %% This lex program echoes numbers divisible by 3 The same thing we've already done with Java and with egrep The lex variable yytext gives us a way to access the substring that matched the regexp Formal Language, chapter 8, slide 38 38
Larger Applications For simple applications, the code produced by lex can be compiled as a stand-alone program, as in the previous examples For most large applications, the code produced by lex is one of many source files from which the full program is compiled Compilers are sometimes written this way: lex generates some source Other tools (like yacc) generate some source Some is written by hand Formal Language, chapter 8, slide 39 39